On the calculation of surface energies

A simple formalism based on response theory is used to evaluate expressions for the surface energy of a uniform dielectric or metallic medium and the change in surface energy of a dielectric solvent when a dilute electrolyte is dissolved in it. The latter result coincides with the result of Onsager and Samaras.     

On the calculation of Auger energies

“Frozen-orbital” expressions within an average-energy formalism are presented for the calculation of Auger transition energies based on the orbitals determined for the initial state. Trial calculations at the minimal-basis level are reported for the K-LL transition in Ne, Na and Mg. We also discuss an ambiguity in the use of certain models for the calculation of both semi-empirical and ab initio Auguer energies. For illustration we give some numerical data on the atoms Ne, Na, Mg and S.     

Linear-scaling formation of Kohn-Sham Hamiltonian: application to the calculation of excitation energies and polarizabilities of large molecular systems

We present calculations of excitation energies and polarizabilities in large molecular systems at the local-density and generalized-gradient approximation levels of density-functional theory (DFT). Our results are obtained using a linear-scaling DFT implementation in the program system DALTON for the formation of the Kohn-Sham Hamiltonian. For the Coulomb contribution, we introduce a modification of the fast multipole method to calculations over Gaussian charge distributions. It affords a simpler implementation than the original continuous fast multipole method by partitioning the electrostatic Coulomb interactions into "classical" and "nonclassical" terms which are explicitly evaluated by linear-scaling multipole techniques and a modified two-electron integral code, respectively. As an illustration of the code, we have studied the singlet and triplet excitation energies as well as the static and dynamic polarizabilities of polyethylenes, polyenes, polyynes, and graphite sheets with an emphasis on the trends observed with system size.     

On the calculation of energies of excited states

We reformulate a scheme for calculation of the energies of excited states which, unlike the variation method, does not require that the trial function be orthogonalized to the wavefunctions for lower excited states. The possibility of obtaining wavefunctions as well as energies is discussed, and an example of the scheme's application is made to the harmonic oscillator.

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Zusammenfassung Es wird eine neue Form für eine Methode zur Berechnung von angeregten Zuständen gegeben. Die Probefunktion braucht nicht wie bei der Variationsmethode orthogonal zu den Wellenfunktionen der tiefer liegenden Zuständen zu sein. Es wird die Möglichkeit diskutiert, Wellenfunktionen ebenso wie Energien zu erhalten. Das Schema wird auf den harmonischen Oszillator angewandt.

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Resume On donne une nouvelle forme pour une methode de calcul des niveaux excités. La methode ne demande pas l'orthogonalisation de la fonction d'essai par rapport aux fonctions d'onde correspondant aux niveaux inférieurs, ce qui montre un avantage auprès de la methode variationnelle. La possibilité d'obtenir les fonctions d'onde elles-mêmes est discutée, et on donne un exemple de l'application de cette nouvelle methode.

     

Molecular applications of the intermediate Hamiltonian Fock-space coupled-cluster method for calculation of excitation energies

The intermediate Hamiltonian Fock-space coupled-cluster (FS-CC) method with singles and doubles is applied to calculate vertical excitation energies (EEs) for some molecular systems. The calculations are performed for several small molecules, such as H2O, N2, and CO, and for larger systems, such as C2H4, C4H6, and C6H6. Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, and the efficient factorization strategy, relatively large basis sets and model spaces are employed permitting a comparison of the calculated vertical EEs with the experimental data.     

On the calculation of activation energies using a modified Kissinger method

Augis and Bennett (J. Thermal Anal. 13 (1978) 283.) [6] recently proposed a modified Kissinger method for determining the activation energy of a transformation. It is shown that the proposed method was, in fact, based upon a modification to the equation for the rate of reaction under non-isothermal conditions. The apparent discrepancy between the proposed method and the original Kissinger method is therefore resolved. The modified rate equation appears to have, at best, only a limited application. However, if the equation should be appropriate for a particular transformation, it is demonstrated that Augis and Bennett's method would be the correct method for determining the activation energy.

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Zusammenfassung Von Augis und Bennett (J. Thermal Anal.13, (1978) 283) wurde eine modifizierte Kissinger-Methode zur Bestimmung der Aktivierungsenergie einer Umwandlung vorgeschlagen. Es wird gezeigt, dass die vorgeschlagene Methode tatsächlich in einer Modifizierung der Gleichung für die Reaktionsgeschwindigkeit unter nicht-isothermen Bedingungen ihren Ursprung hat. Die scheinbare Diskrepanz zwischen der vorgeschlagenen Methode und der ursprünglichen Kissinger-Methode wird dadurch behoben. Die modifizierte Geschwindigkeitsgleichung hat bestenfalls nur eine begrenzte Anwendung. Jedoch, bei Eignung dieser Gleichung für eine bestimmte Umwandlung zeigt sich, dass die Methode von Augis und Bennett die richtige Methode zur Bestimmung der Aktivierungsenergie sein kann.

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(J. Thermal Anal. 13 (1978) 283.) - . , , , . , . , , , . , , .

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The author is indebted to the Senate of the University of Queensland for the award of a University Research Fellowship; and to Professor R. R. Stephens for providing laboratory facilities.     

New possibilities of Möller-Plesset perturbation theory for calculating correlation energies of closed-shell systems

A new scheme for generating and selecting configurational wave functions (CWF) including the correlation effects is suggested. Standard Möller-Plesset perturbation theory (SMP) is modified in such a way that the newly constructed CWF and the Hartree-Fock reference determinant are the eigenfunctions of a zero-order Hamiltonian. Possessing all advantages of SMP, the calculation scheme allows for more than 80% of the empirical correlation energy in the second order. The results for diatomic hydrides are comparable in accuracy to those obtained by the configuration interaction method.     

On the calculation of correlation energies in the spin-density functional formalism

It is shown that dynamical correlation effects can be adequately treated using the local spin-density approximation. The computational effort is very small compared to CI calculations. The method is applied to correlation energies and ionization potentials of the atoms Li to Ar and binding energies of the diatomic hydrides LiH to HCl.     

On the calculation of multiplet energies by the hartree-fock-slater method

It is shown that a consistent application of the p ^1/3 approximation of the Hartree-Fock-Slater method requires the use of one specific procedure, the sum method, for the calculation of the energy E _s ¹ of singlet excited states of closed shell molecules. Further, E _s ¹ is found to be in reasonable agreement with experiment for a number of molecules, contrary to the energy E _s ² obtained according to another method discussed in the literature. The calculation of other multiplet splittings than singlet-triplet in the Hartree-Fock-Slater method is also considered.     

Intermediate Hamiltonian Fock-space multireference coupled-cluster method with full triples for calculation of excitation energies

The intermediate Hamiltonian multireference coupled-cluster (CC) method with singles, doubles, and triples within the excited (1,1) sector of Fock space (FS) is implemented and formulated to calculate excitation energies (EEs). Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, coupled to an efficient factorization strategy, relatively large basis sets and model spaces are employed permitting basis set converged comparisons of the calculated vertical EEs, which can be compared to the experimental data for the N(2) and CO molecules. The issue of charge-transfer separability is also addressed.     

Exchange polarization effects in the interaction of closed-shell systems

Explicit formulae for the calculation of the exchange polarization energy in the interaction of closed-shell atoms or molecules have been derived by assuming neglect of the electron correlation within the noninteracting systems. The dispersion part of the exchange polarization energy has been represented as a sum of contributions arising from the interaction of two, three or four orbitals at a time. Each of these contributions is given by an integral involving the orbitals engaged in the interaction and the pair functions describing the dispersion interaction between these orbitals. The numerical calculations for the interaction of two ground-state beryllium atoms show that the exchange dispersion energy is positive and quenches about 5 to 10 per cent of the dispersion term. This results in a decrease of the interaction energy, computed as a sum of the SCF and dispersion components, by 6 to 30 per cent for interatomic distances ranging from 10 to 7 bohrs.Simplified formulae for estimating the exchange dispersion energy in the interaction of larger systems are also proposed and their accuracy is discussed.     

Calculation of vertical excitation energies of closed-shell molecules in the CNDO and INDO approximations

The Green's function method for the calculation of vertical excitation energies is adapted to the CNDO and INDO approximations by introducing an effective interaction into the irreducible vertex part. The computational scheme is explicitly developed for closed-shell molecules and applied to H₂O, H₂CO, HCOOH, HCONH₂.     

New method for the direct calculation of electron density in many-electron systems. I. Application to closed-shell atoms

Analytical properties of hydrogen-like atomic orbitals (HAO ) that are used in the MOLCAO approach to the quantum theory of molecules have been studied. Addition and expansion theorems for HAO have been proved, both in coordinate and momentum representations. A close relation has been established between HAO and the reduced Bessel functions of half-integer indices. New methods are suggested to calculate integrals for atomic and molecular form factors, and multicenter integrals, for the HAO basis in the MO LCAO theory.     

Application of one-particle Green functions technique for calculation of vertical ionization potentials of closed-shell molecules described by CNDO/2 semiempirical Hamiltonian

A simple method of infinite summations of some dominant diagrams in the framework of the one-particle Green functions technique is suggested. This method for the calculation of the lowlying vertical ionization potentials of some simple closed-shell molecules described by CNDO/2 semiempirical Hamiltonian is applied. The obtained results are in quite-satisfactory agreement with the experimental values of the vertical ionization potentials measured by the photo-electron spectroscopy technique.     

On the calculation of bonding energies by the Hartree Fock Slater method

A transition state method has been proposed for the calculation of bonding energies and bond distances within the Hartree Fock Slater Method. Calculations on a number of diatomic molecules and a few transition metal complexes show better agreement with experiment than corresponding Hartree Fock results. The proposed transition state method gives a direct connection between bond orders and bonding energies.     

On the calculation of a limit for infinite systems from data on finite systems

We propose a mathematical model for the calculation of physical or chemical properties of infinite polymers, based on data for structurally closely related finite molecules. The modelling is phenomenological but permits a physical interpretation of the parameters involved in the equations. Received: 11 June 1996 / Accepted: 5 June 1997     

A note on the orbital energy-splitting of closed-shell systems in the DODS scheme

Investigating the lowering of the total energy and the orbital energy-splittings of electrons with spins α and β, respectively, in the DODS scheme, ab initio calculations have been performed for the formaldehyde molecule. The results obtained by changing the CO distance and the orbital exponents of the C and O atoms indicate that the decrease of the electron density in the CO bond region causes larger orbital energy-splittings and lowering of the energy.